Dislocation core radii near elastic stability limits

Abstract

Recent studies of transition metal alloys with compositions that place them near their limits of elastic stability (e.g. near the body-centered-cubic [BCC] to hexagonal-close-packed [HCP] transition) suggest interesting behavior for the dislocation cores. Specifically, the dislocation core size is predicted to diverge as the stability limit is approached. Here a simple analysis rooted in elasticity theory and the computation of ideal strength is used to analyze this divergence. This analysis indicates that dislocation core radii should diverge as the elastic limits of stability are approached in the BCC, HCP, and face-centered-cubic (FCC) structures. Moreover, external stresses and dislocationinduced stresses also increase the core radii. Density functional theory based total energy calculations are combined with anisotropic elasticity theory to compute numerical estimates of dislocation core radii.

Dependence of mechanical properties on the site occupancy of ternary alloying elements in γ′-Ni3Al: Ab initio description for shear and tensile deformation*

“…Dominated by the behavior of chemical bonding, common slip, and nucleation of dislocations, [53][54][55] the ideal strength of solid materials sets the upper bound of the strength achievable by a real material under certain loading conditions. Investigations of the ideal strength are fundamental to understand the behavior of fracture, failure, [56][57][58] and creep [59,60] for advanced materials as well as to determine the gap between the real strength of materials and their ideal strength. [61] Ab initio computational [110] tensile and {111} 11 2 shear tests were implemented in stoichiometric Ni 3 Al, and the ideal strength and corresponding strains calculated according to Eqs.…”

Lattice stability and the effect of Co and Re on the ideal strength of Ni: First-principles study of uniaxial tensile deformation

“…[2] For example, in some special materials, the width of the dislocation core is related to the size of its ideal shear strength, and the local stress of cleavage crack nucleation must be greater than its ideal uniaxial tensile strength. [3][4][5] The ideal strength sets an upper bound for the strength of a real material. The simplest approach to determine the ideal strength is calculating the stress-strain curve of a system in the deformation process, and takes the first maximum or minimum point of the stress-strain curves as the ideal strength of materials.…”

Dislocations near elastic instability in high-pressure body-centered-cubic magnesium

“…By defining the dislocation core as the region for which the stress predicted by linear elasticity theory is greater than the ideal strength, an approximation for the region in which linear elasticity theory is no longer valid is obtained. 6,7 Since symmetry often links the ideal strength to the elastic constants, this definition allows for the dislocation core radius to be written in terms of the elastic constants. In the case of a BCC metal the dislocation core radius can be expressed as…”

“…Subsequent work on Gum Metal suggested that a more general connection can be made between the properties of Gum Metal and the proximity of a material to an elastic instability. [5][6][7][8] Gum Metals exist near the composition at which the body-centered cubic (BCC) phase becomes elastically unstable and transforms into the hexagonal close-packed (HCP) phase. The proximity to this lattice instability is apparent in the elastic constants.…”

“…7 In fact, experimentally the BCC to face-centered cubic (FCC) instability has been exploited to produce a Fe-Ni-Co-Ti alloy with Gum Metal like properties. In what follows, we consider the potential for a non-transition metal to display properties that have been linked to the "super" properties of TiNb based Gum Metals.…”